# std::ranges::is_permutation

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< cpp‎ | algorithm‎ | ranges

Defined in header `<algorithm>` |  |
Call signature |  |
template< std::forward_iterator I1, std::sentinel_for<I1> S1, std::forward_iterator I2, std::sentinel_for<I2> S2, class Proj1 = std::identity, class Proj2 = std::identity, std::indirect_equivalence_relation<std::projected<I1, Proj1>, std::projected<I2, Proj2>> Pred = ranges::equal_to > constexpr bool is_permutation( I1 first1, S1 last1, I2 first2, S2 last2, Pred pred = {}, Proj1 proj1 = {}, Proj2 proj2 = {} ); | (1) | (since C++20)
template< ranges::forward_range R1, ranges::forward_range R2, class Proj1 = std::identity, class Proj2 = std::identity, std::indirect_equivalence_relation< std::projected<ranges::iterator_t<R1>, Proj1>, std::projected<ranges::iterator_t<R2>, Proj2>> Pred = ranges::equal_to > constexpr bool is_permutation( R1&& r1, R2&& r2, Pred pred = {}, Proj1 proj1 = {}, Proj2 proj2 = {} ); | (2) | (since C++20)

1) Returns true if there exists a permutation of the elements in range `[`first1`,` last1`)` that makes the range equal to `[`first2`,` last2`)` (after application of corresponding projections Proj1, Proj2, and using the binary predicate Pred as a comparator). Otherwise returns false.
2) Same as (1), but uses r1 as the first source range and r2 as the second source range, as if using ranges::begin(r1) as first1, ranges::end(r1) as last1, ranges::begin(r2) as first2, and ranges::end(r2) as last2.

The function-like entities described on this page are algorithm function objects (informally known as niebloids), that is:

- Explicit template argument lists cannot be specified when calling any of them.
- None of them are visible to argument-dependent lookup.
- When any of them are found by normal unqualified lookup as the name to the left of the function-call operator, argument-dependent lookup is inhibited.

### Parameters

first1, last1 | - | the first range of the elements
first2, last2 | - | the second range of the elements
r1 | - | the first range of the elements
r2 | - | the second range of the elements
pred | - | predicate to apply to the projected elements
proj1 | - | projection to apply to the elements in the first range
proj2 | - | projection to apply to the elements in the second range

### Return value

true if the range `[`first1`,` last1`)` is a permutation of the range `[`first2`,` last2`)`.

### Complexity

At most \(\scriptsize \mathcal{O}(N^2)\)O(N2) applications of the predicate and each projection, or exactly \(\scriptsize N\)N if the sequences are already equal, where \(\scriptsize N\)N is ranges::distance(first1, last1). However if ranges::distance(first1, last1) != ranges::distance(first2, last2), no applications of the predicate and projections are made.

### Notes

The permutation relation is an equivalence relation.

The `ranges::is_permutation` can be used in testing, e.g. to check the correctness of rearranging algorithms such as sorting, shuffling, partitioning. If `p` is an original sequence and `q` is a "mutated" sequence, then ranges::is_permutation(p, q) == true means that `q` consist of "the same" elements (maybe permuted) as `p`.

### Possible implementation

    struct is_permutation_fn
    {
        template<std::forward_iterator I1, std::sentinel_for<I1> S1,
                 std::forward_iterator I2, std::sentinel_for<I2> S2,
                 class Proj1 = std::identity, class Proj2 = std::identity,
                 std::indirect_equivalence_relation<std::projected<I1, Proj1>,
                                                    std::projected<I2, Proj2>>
                                                        Pred = ranges::equal_to>
        constexpr bool operator()(I1 first1, S1 last1, I2 first2, S2 last2,
                                  Pred pred = {}, Proj1 proj1 = {}, Proj2 proj2 = {}) const
        {
            // skip common prefix
            auto ret = std::ranges::mismatch(first1, last1, first2, last2,
                                             std::ref(pred), std::ref(proj1), std::ref(proj2));
            first1 = ret.in1, first2 = ret.in2;

            // iterate over the rest, counting how many times each element
            // from [first1, last1) appears in [first2, last2)
            for (auto i {first1}; i != last1; ++i)
            {
                const auto i_proj {std::invoke(proj1, *i)};
                auto i_cmp = [&]<typename T>(T&& t)
                {
                    return std::invoke(pred, i_proj, std::forward<T>(t));
                };

                if (i != ranges::find_if(first1, i, i_cmp, proj1))
                    continue; // this *i has been checked

                if (const auto m {ranges::count_if(first2, last2, i_cmp, proj2)};
                    m == 0 or m != ranges::count_if(i, last1, i_cmp, proj1))
                    return false;
            }
            return true;
        }

        template<ranges::forward_range R1, ranges::forward_range R2,
                 class Proj1 = std::identity, class Proj2 = std::identity,
                 std::indirect_equivalence_relation<
                     std::projected<ranges::iterator_t<R1>, Proj1>,
                     std::projected<ranges::iterator_t<R2>, Proj2>>
                         Pred = ranges::equal_to>
        constexpr bool operator()(R1&& r1, R2&& r2, Pred pred = {},
                                  Proj1 proj1 = {}, Proj2 proj2 = {}) const
        {
            return (*this)(ranges::begin(r1), ranges::end(r1),
                           ranges::begin(r2), ranges::end(r2),
                           std::move(pred), std::move(proj1), std::move(proj2));
        }
    };

    inline constexpr is_permutation_fn is_permutation {};

### Example

Run this code

    #include <algorithm>
    #include <array>
    #include <cmath>
    #include <iostream>
    #include <ranges>

    auto& operator<<(auto& os, std::ranges::forward_range auto const& v)
    {
        os << "{ ";
        for (const auto& e : v)
            os << e << ' ';
        return os << "}";
    }

    int main()
    {
        static constexpr auto r1 = {1, 2, 3, 4, 5};
        static constexpr auto r2 = {3, 5, 4, 1, 2};
        static constexpr auto r3 = {3, 5, 4, 1, 1};

        static_assert(
            std::ranges::is_permutation(r1, r1) &&
            std::ranges::is_permutation(r1, r2) &&
            std::ranges::is_permutation(r2, r1) &&
            std::ranges::is_permutation(r1.begin(), r1.end(), r2.begin(), r2.end()));

        std::cout
            << std::boolalpha
            << "is_permutation(" << r1 << ", " << r2 << "): "
            << std::ranges::is_permutation(r1, r2) << '\n'
            << "is_permutation(" << r1 << ", " << r3 << "): "
            << std::ranges::is_permutation(r1, r3) << '\n'

            << "is_permutation with custom predicate and projections: "
            << std::ranges::is_permutation(
                std::array {-14, -11, -13, -15, -12},  // 1st range
                std::array {'F', 'E', 'C', 'B', 'D'},  // 2nd range
                [](int x, int y) { return abs(x) == abs(y); }, // predicate
                [](int x) { return x + 10; },          // projection for 1st range
                [](char y) { return int(y - 'A'); })   // projection for 2nd range
            << '\n';
    }

Output:

    is_permutation({ 1 2 3 4 5 }, { 3 5 4 1 2 }): true
    is_permutation({ 1 2 3 4 5 }, { 3 5 4 1 1 }): false
    is_permutation with custom predicate and projections: true

### See also

ranges::next_permutation (C++20) | generates the next greater lexicographic permutation of a range of elements (algorithm function object)
ranges::prev_permutation (C++20) | generates the next smaller lexicographic permutation of a range of elements (algorithm function object)
is_permutation (C++11) | determines if a sequence is a permutation of another sequence (function template)
next_permutation | generates the next greater lexicographic permutation of a range of elements (function template)
prev_permutation | generates the next smaller lexicographic permutation of a range of elements (function template)
equivalence_relation (C++20) | specifies that a `relation` imposes an equivalence relation (concept)

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